They're not interchangeable. "Run out" means your supply has been exhausted. You have no more. If you "run out of fuel", there's no fuel left.
In this context, "run through" is usually followed by "a lot." If you "run through a lot of fuel", you use it up quickly. You may or may not have some left right now, but that's not what we're focusing on. We're focusing on the rate at which you use it.